A meet in a frame is exact if it join-distributes with every element, it is strongly exact if it is preserved by every frame homomorphism. Hence, finite meets are (strongly) exact which leads to the concept of an exact resp. strongly exact filter, a filter closed under exact resp. strongly exact meets. It is known that the exact filters constitute a frame FiltE(L) somewhat surprisingly isomorphic to the frame of joins of closed sublocales. In this paper we present a characteristic of the coframe of meets of open sublocales as the dual to the frame of strongly exact filters FiltsE(L).
Moshier, M.A., Pultr, A. & Suarez, A.L. Exact and Strongly Exact Filters. Appl Categor Struct (2020). https://doi.org/10.1007/s10485-020-09602-0
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